Model Order Reduction Techniques for Nonlinear Cross-Diffusion Systems With Rational Reaction Functions

Gülden Mülayim

Journal of Mathematics, 2026, vol. 2026, 1-12

Abstract: This study employs the Shigesada–Kawasaki–Teramoto (SKT) model with rational reaction terms as a benchmark for reduced-order models (ROMs) of nonlinear cross-diffusion systems. Full-order models (FOMs) are derived through temporal discretization using an implicit-symplectic (IMSP) scheme and spatial discretization via the finite difference methods. Both FOMs and ROMs share a unified construction framework. To compute ROM solutions, the proper orthogonal decomposition (POD) method is first applied, followed by the discrete empirical interpolation method (DEIM) to handle nonlinear terms efficiently. The Q-DEIM technique is further integrated to enhance numerical robustness. The efficacy of the ROM solutions is validated through numerical experiments in both one- and two-dimensional domains.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1582888

DOI: 10.1155/jom/1582888

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